# Demographics and Asset Prices: The Murder-Suicide of the Rentier

## 1. Introduction

Population aging reshapes the macroeconomic landscape through its effects on savings, investment, and capital flows. A growing literature documents that demographic structure predicts current account balances across countries, but far less attention has been paid to the asset price implications. This paper tests whether demographic structure systematically predicts asset returns and valuations across countries, spanning safe interest rates, term structure, real effective exchange rates, house prices, and equity market capitalization.

Our theoretical framework draws on Kopecky and Taylor (2022), who describe the "murder-suicide of the rentier": as populations age, elderly savers crowd into safe assets (bonds), depressing safe returns, while simultaneously withdrawing from risky assets (equities), sustaining or even widening the equity risk premium. The net effect is a collapse in the risk-free rate without a corresponding decline in equity returns — the "murder" of safe returns and the "suicide" of the rentier class that depends on them.

We employ the demographic polynomial approach of Higgins (1998) and Koomen (2021), constructing three orthogonal demographic components ($Z_1$, $Z_2$, $Z_3$) that capture the age-structure of each country's population. Using a panel of up to 237 countries over 1950-2024, we estimate pooled GLS models with AR(1) correction for each asset class.

Our key findings are: (1) demographics strongly predict real interest rates, with $Z_1$ coefficients of 43.7 ($p = 0.015$) for 10-year bonds and 60.1 ($p = 0.004$) for 3-month rates — countries with larger working-age shares have higher equilibrium safe rates; (2) the term spread does not respond to demographics ($p = 0.36$), despite its significance in current account regressions (our companion multilateral paper), implying that term spread variation in CA models captures monetary policy or inflation credibility rather than demographic channels; (3) demographic structure has weak direct effects on real effective exchange rates, but the Z-NFA interaction is significant ($p = 0.010$ with lagged NFA), suggesting demographics amplify the exchange rate effects of creditor/debtor positions; (4) house price growth shows no significant response to the demographic polynomial ($p = 0.63$), and apparent age-decomposition effects collapse entirely when GDP per capita is controlled — housing is not among the asset classes that respond to demographics; and (5) stock market capitalization shows no demographic sensitivity ($p = 0.92$), while safe rates are strongly predicted — consistent with the Kopecky-Taylor "murder-suicide" asymmetry. We do not directly estimate the equity risk premium; we test an implication of the framework for equity valuation proxies and find it consistent. Importantly, Z-KAOPEN interactions are null for safe rates ($p > 0.71$), even though they are highly significant for current account balances ($p < 0.005$) in the companion papers. This distinction reveals that demographics affect domestic asset prices regardless of financial openness, while capital account openness gates only the international flow channel.

## 2. Data

### 2.1 Panel Construction

Our base panel draws from the multilateral demographics and capital flows dataset, covering 237 countries from 1950 to 2024 (17,775 country-year observations). We augment this with three additional data sources targeting asset prices.

**BIS Real Effective Exchange Rates.** We obtain broad CPI-based real effective exchange rate indices from the Bank for International Settlements, covering 57 economies at monthly frequency. We annualize by taking calendar-year averages and construct log levels ($\log \text{REER}$) and annual percentage changes ($\Delta \text{REER}$), yielding 1,881 country-year observations.

**BIS Residential Property Prices.** The BIS Selected Property Prices dataset provides real (CPI-deflated) residential property price growth rates (year-on-year, percent) for 56 economies at quarterly frequency, predominantly OECD members. We annualize by taking calendar-year averages, yielding 1,982 country-year observations (1,499 with complete controls for 56 countries in the expanded panel). The series has mean 4.6% and standard deviation 8.4%, ranging from $-37.9$% to $+94.7$% — consistent with known episodes of house price booms and busts across OECD economies.

**World Bank Stock Market Capitalization.** Stock market capitalization as a percentage of GDP (indicator CM.MKT.LCAP.GD.ZS) from the World Development Indicators covers 35 economies (1,032 observations). We also obtain stocks traded as a percentage of GDP (37 economies, 1,103 observations).

The base panel already contains: real 10-year government bond yields, real 3-month rates, term spreads, carry trade measures, cross-border portfolio equity positions, and gross international financial positions from the IMF. Real bond yields and real short rates are computed as nominal rates minus contemporaneous CPI inflation (ex post real rates).

### 2.2 Data Coverage and Quality

While the base panel covers 237 countries, asset price data are concentrated in advanced and upper-middle-income economies. The following table summarizes effective coverage by asset class:

| Asset Class | Source | Countries | Obs. | Coverage |
|---|---|---:|---:|---|
| Real 10y bond yield | IMF/WDI | 23 | 803 | OECD only |
| Real 3m rate | IMF/WDI | 23 | 813 | OECD only |
| Term spread | Computed | 23 | 781 | OECD only |
| REER | BIS | 57 | 1,881 | Broad (OECD + 20 EM) |
| House prices | BIS | 56 | 1,982 | OECD + select EM |
| Stock mkt cap/GDP | WDI | 35 | 1,032 | OECD + upper-middle |
| Portfolio equity/GDP | IMF CPIS | 136 | 4,275 | Broad |

The critical safe rate results (Sections 3–4) are estimated on 23 OECD economies with reliable government bond markets. No results in this paper are driven by imputed or interpolated values in frontier markets. The 237-country coverage applies only to the demographic variables themselves and to cross-border portfolio positions (IMF CPIS), which have broad reporting. For housing and equity capitalization, the effective samples are 23 and 35 countries respectively — small panels where individual country influence warrants scrutiny (addressed in Section 9.5).

### 2.3 Demographic Variables

We follow the polynomial approach of Higgins (1998). The population age distribution is projected onto orthogonal polynomial bases, yielding three components:

$$Z_{1,it} = \sum_{k=1}^{K} \phi_{1k} \cdot d_{n,k,it}$$

where $d_{n,k,it}$ is the normalized share of population in age group $k$ for country $i$ in year $t$, and $\phi_{1k}$ are the first polynomial weights. $Z_1$ captures the broad lifecycle savings pattern (positive for working-age-heavy populations), $Z_2$ captures the hump shape, and $Z_3$ captures higher-order variation.

We also decompose demographics into old-age dependency (population 65+/working age) and youth dependency (population 0-14/working age) to test opposing channel predictions.

## 3. Safe Rates and Term Structure

### 3.1 Baseline Results

The Kopecky-Taylor framework predicts that aging depresses safe rates as elderly savers crowd into bonds. We test this directly:

$$r_{it}^{safe} = \gamma_1 Z_{1,it} + \gamma_2 Z_{2,it} + \gamma_3 Z_{3,it} + \beta' X_{it} + u_{it}$$

where $r^{safe}$ is the real 10-year government bond yield or real 3-month rate, and controls include GDP growth, inflation, fiscal balance/GDP, capital account openness (KAOPEN), and lagged NFA/GDP.

Results strongly confirm the prediction. For real 10-year bond yields ($N = 803$, 23 countries, $R^2 = 0.108$):

- $Z_1 = 43.72$ (SE = 18.01, $p = 0.015$)
- $Z_2 = -4.63$ (SE = 2.37, $p = 0.051$)

For real 3-month rates ($N = 813$, 23 countries, $R^2 = 0.005$):

- $Z_1 = 60.07$ (SE = 20.98, $p = 0.004$)
- $Z_2 = -7.01$ (SE = 2.78, $p = 0.012$)
- $Z_3 = 0.23$ (SE = 0.10, $p = 0.030$)

The positive $Z_1$ coefficient indicates that countries with larger working-age shares have higher safe rates, while aging populations see safe rate compression. The short rate ($Z_1 = 60.1$) is more sensitive to demographics than the long rate ($Z_1 = 43.7$).

An important question is whether this reflects the Kopecky-Taylor portfolio rebalancing mechanism (aging → bond demand → yield compression) or a supply-side channel (larger workforce → higher investment demand → higher equilibrium rate). Both predict the same sign. We probe the distinction by adding gross investment/GDP as a control. If the rate result is primarily supply-side, controlling for investment should absorb the demographic effect. Instead, $Z_1$ *strengthens* slightly from 43.7 ($p = 0.015$) to 48.0 ($p = 0.007$) when investment/GDP is included, while investment itself enters with a negative coefficient ($-0.044$). The result is similar with minimal controls: with only GDP growth and investment/GDP, $Z_1 = 51.9$ ($p = 0.001$), while investment enters with a highly significant coefficient ($-0.180$, $p < 0.001$). The demographic polynomial captures portfolio and savings behavior that is not obviously mediated by contemporaneous investment. We note the caveat that investment/GDP is itself an equilibrium object — it responds to the same demographic forces that drive savings — so this test is suggestive rather than definitive. Nevertheless, the stability of $Z_1$ across specifications with and without investment controls is consistent with the Kopecky-Taylor demand-side interpretation.

The fact that countries with higher $Z_1$ simultaneously have higher rates *and* run current account surpluses (as shown in our companion multilateral paper) is consistent: the portfolio rebalancing channel depresses rates in aging economies while the excess savings flow abroad as current account surpluses.

The age decomposition confirms the channel: old-age dependency is strongly negative ($-16.93$, $p < 0.001$) and youth dependency is strongly positive ($+17.25$, $p = 0.004$) on real 10-year yields ($R^2 = 0.139$), consistent with lifecycle theory.

**The term spread inconsistency.** The term spread ($N = 781$, 23 countries, $R^2 = 0.139$) does not respond significantly to $Z_1$ ($p = 0.39$). This is one of the paper's most informative results. Our companion multilateral paper finds that the term spread is a highly significant predictor of current account balances ($p < 0.001$), yet demographics do not predict the term spread itself. The implication is that term spread variation in CA regressions captures monetary policy regime differences or inflation credibility — factors that correlate with demographic structure but are not caused by it. This distinction matters for the Kopecky-Taylor framework: demographics affect the *level* of safe rates at both maturities, but the *slope* of the yield curve is driven by non-demographic factors. The inconsistency also serves as a disciplining device: it rules out the possibility that our demographic polynomials are simply proxying for a general "macroeconomic maturity" effect that predicts all financial variables.

### 3.2 OECD Subsample

The rate channel is confirmed on the 23-country OECD sample (all available bond yield data comes from OECD economies), consistent with our prior finding that bond yields respond to demographics only in economies with deep, liquid bond markets.

### 3.3 Lagged and First-Differenced Specifications

To address reverse causality, we estimate models with 5-year lagged demographics. The lagged specification strengthens the results: $Z_{1,t-5} = 52.16$ ($p < 0.001$), $Z_{2,t-5} = -6.11$ ($p = 0.003$), $Z_{3,t-5} = 0.20$ ($p = 0.013$), with $R^2 = 0.155$. Past demographics predict current rates more strongly than contemporaneous demographics, supporting a causal interpretation and suggesting the portfolio rebalancing mechanism operates with a lag.

The first-differenced specification ($\Delta Z \to \Delta r$) yields insignificant demographic coefficients ($R^2 = 0.654$ driven by $\Delta$inflation), indicating that the demographic effect operates through slow-moving levels rather than year-to-year changes — consistent with the structural lifecycle mechanism rather than short-run cyclical variation.

### 3.4 Z-KAOPEN Interactions

There is no robust evidence that capital account openness moderates the demographic effect on safe rates. The $Z_1 \times \text{KAOPEN}$ interaction is insignificant ($p = 0.71$), with some borderline interactions for the 3-month rate ($p \approx 0.06$-$0.08$) that are not stable across specifications. This stands in sharp contrast to the companion multilateral and gravity papers, where Z-KAOPEN interactions are highly significant ($p < 0.005$) for current account balances and bilateral portfolio flows. The contrast is informative: demographics affect domestic safe rates regardless of whether the capital account is open, but capital account openness gates whether the resulting savings imbalance translates to international capital flows. The rate channel is a domestic portfolio story; the flow channel requires open borders. This also explains why the gravity bilateral paper finds that 58% of the demographic effect on bilateral flows is rate-mediated — demographics move rates, which then incentivize cross-border flows conditional on openness — while the rate effect itself is unconditional on openness.

## 4. Real Exchange Rates

### 4.1 Demographic Channels to REER

Aging economies tend to run current account surpluses, which should put upward pressure on the real exchange rate. We test:

$$\log \text{REER}_{it} = \gamma' Z_{it} + \beta' X_{it} + u_{it}$$

Using 1,572 observations across 55 countries ($R^2 = 0.028$), demographic components are not individually significant ($Z_1$: $p = 0.31$). The exchange rate results are notably weaker than the safe rate channel, suggesting demographics affect asset markets more directly through portfolio composition than through the exchange rate.

### 4.2 Z-NFA Interaction

While demographics alone do not predict REER, their interaction with net foreign asset positions is significant. Using lagged NFA/GDP to reduce simultaneity: $Z_1 \times \text{NFA}_{t-1} = -1.17$ ($p = 0.010$), $Z_2 \times \text{NFA}_{t-1} = 0.15$ ($p = 0.022$), $Z_3 \times \text{NFA}_{t-1} = -0.006$ ($p = 0.033$). Demographics amplify the exchange rate effects of creditor/debtor positions: aging creditor nations see greater real appreciation, while aging debtor nations see depreciation. The contemporaneous NFA interaction is also significant ($Z_1 \times \text{NFA}$: $p = 0.025$), strengthening the interpretation. However, we note that NFA is itself endogenous to prior demographic-driven flows, so this result should be interpreted as a conditional correlation rather than a causal estimate.

### 4.3 Capital Account Openness and Carry Trade

The Z-KAOPEN interactions are not significant for REER ($p > 0.3$). Demographics also fail to predict carry trade returns ($Z_1$: $p = 0.49$), suggesting the exchange rate channel is not the primary mechanism through which demographics affect asset returns.

## 5. Housing Markets

### 5.1 Demographic Structure and House Prices

Housing is the dominant asset for most households. We estimate:

$$\Delta \text{RHPI}_{it} = \gamma' Z_{it} + \beta' X_{it} + u_{it}$$

Using 1,499 observations across 56 countries ($R^2 = 0.005$), the demographic polynomial components are not individually significant ($Z_1$: $p = 0.63$). The lifecycle savings pattern that strongly predicts safe rates does not predict house prices.

The age decomposition reveals a potential spurious channel. In the raw specification, old-age dependency is positive and significant ($+6,614$, $p = 0.030$) and youth dependency is strongly positive ($+11,758$, $p = 0.001$). However, adding log GDP per capita as a control collapses both coefficients entirely: old-age dependency becomes null ($+1,129$, $p = 0.293$) and youth dependency vanishes ($-85$, $p = 0.946$). The apparent demographic effect on housing operates through income levels, not through a direct demographic channel. The overall conclusion is that demographics do not have a robust direct effect on house prices once the GDP per capita confound is controlled.

### 5.2 Limited Coverage and Post-GFC

BIS house price data cover predominantly OECD economies, limiting the sample to 23 countries with complete controls. The post-GFC subsample (2010+, $N = 322$) shows no significant demographic effects ($Z_1 = 0.50$, $p = 0.99$), with all demographic variation absorbed by the interest rate and inflation controls that dominate post-GFC house price dynamics ($R^2 = 0.298$). The housing result is weak at best: the demographic polynomial is null, and the marginal youth dependency effect does not survive all specifications.

## 6. Equity Markets

### 6.1 Stock Market Capitalization

The Kopecky-Taylor prediction is that equity markets should be *less* sensitive to demographics than safe rates. We do not directly estimate the equity risk premium; rather, we test an implication of the framework for equity valuation proxies. Using stock market capitalization/GDP — which reflects listings, free-float conventions, buyback activity, and corporate leverage in addition to fundamental valuations — across 779 observations and 33 countries ($R^2 = 0.180$):

- $Z_1 = 47.2$ (SE = 471.4, $p = 0.920$)

Demographics are completely null for stock market capitalization/GDP. The OECD subsample ($N = 374$, 13 countries) is similarly null ($Z_1 = -150.4$, $p = 0.62$). Changes in stock market capitalization are also null ($p = 0.51$). The Z-KAOPEN interactions are insignificant ($p > 0.5$). The age decomposition (old_dep, youth_dep) is also null ($p > 0.5$).

### 6.2 Cross-Border Equity Positions

Portfolio equity assets/GDP do respond to demographics ($N = 5,435$, 174 countries):

- $Z_1 = -374.5$ ($p < 0.001$)
- $Z_2 = 60.9$ ($p < 0.001$)
- $Z_3 = -2.5$ ($p < 0.001$)

The significance is robust to dropping financial centers (Luxembourg at 1,964% of GDP, Singapore, Hong Kong, etc.) and to winsorizing at p1/p99 — in fact, $Z_1$ *strengthens* after excluding outliers (from $-375$ to $-314$, $p < 0.001$). However, the persistently negative $R^2$ ($-0.029$ to $-0.044$ across specifications) indicates the model has no real explanatory power despite significant coefficients. We treat this as descriptive cross-sectional patterning rather than a substantive finding. CPIS positions are dominated by financial centers, valuation effects, and reporting asymmetries that our specification does not capture. Demographics may capture a real cross-country pattern — aging economies accumulate larger gross international portfolios through lifecycle wealth accumulation — but the model misses the dominant drivers.

### 6.3 The Asymmetry Test

The key Kopecky-Taylor test compares demographic sensitivity of safe rates versus equity within OECD:

| Asset | Z₁ coefficient | p-value |
|-------|---------------|---------|
| Safe rate (10y) | 43.72 | 0.015 |
| Stock mkt cap/GDP | -150.41 | 0.619 |

Demographics are strongly significant for safe rates but completely null for equity capitalization, consistent with the murder-suicide framework's core prediction for valuation proxies. As shown in Section 3.1, the safe rate result survives controlling for investment/GDP, suggesting the demographic effect is not obviously mediated by contemporaneous investment and is consistent with the Kopecky-Taylor portfolio rebalancing mechanism.

The equity null deserves elaboration. If aging populations withdraw from risky assets (the "suicide" of the rentier), why doesn't equity capitalization decline? Three forces offset the demographic withdrawal. First, **institutional replacement**: as individual retail investors age out of equities, pension funds, sovereign wealth funds, and insurance companies step in with mandated equity allocations that are relatively insensitive to the age structure of the underlying beneficiaries. The shift from defined-benefit to defined-contribution pensions in most OECD economies has, if anything, increased institutional equity demand by making individual retirement accounts the default savings vehicle. Second, **international diversification**: aging-economy pension funds allocate increasingly to foreign equities, while young-economy investors — enabled by capital account opening — invest in aging-economy stock markets. Our companion gravity paper documents this bilateral pattern directly: demographic distance (ΔZ) predicts portfolio equity positions (all p < 0.001), with capital flowing from young surplus economies toward aging economies' equity markets. As domestic rentiers exit equities, international investors from demographically younger countries step in, sustaining valuations. Cross-border equity flows partially decouple domestic equity valuations from domestic demographic structure. Our portfolio equity/GDP results (Section 6.2) confirm this at the aggregate level: demographics predict *cross-border* equity positions (p = 0.002) even as domestic capitalization is null. Third, **corporate buybacks and leverage**: in low-rate environments created by the demographic "murder" of safe returns, corporations substitute debt for equity through buybacks, mechanically supporting equity valuations even as underlying demand composition shifts. The murder of safe rates and the resilience of equity are linked: the same demographic savings glut that compresses yields provides cheap corporate borrowing that sustains equity prices.

## 7. Cross-Asset Synthesis: The Murder-Suicide of the Rentier

### 7.1 Standardized Coefficient Comparison

We standardize all dependent variables to unit variance (mean zero, standard deviation one) within each estimation sample and estimate identical specifications with unstandardized $Z$ regressors. The resulting coefficients represent the effect of a one-unit change in $Z_1$ on each outcome measured in standard deviations. To aid interpretation: the interquartile range of $Z_1$ within the OECD rate sample is approximately 0.003, so a shift from the 25th to the 75th percentile of demographic structure corresponds to roughly $0.003 \times 15.3 \approx 0.046$ standard deviations of the 10-year yield — a modest but statistically reliable effect that accumulates through persistence.

The cross-asset demographic sensitivity matrix reveals a clear hierarchy:

| Asset Class | Z₁ (std Y) | p-value | N |
|---|---|---|---|
| Safe rate (3m) | 18.14*** | 0.005 | 813 |
| Safe rate (10y) | 14.72** | 0.015 | 803 |
| Portfolio equity/GDP | -4.86*** | <0.001 | 5,435 |
| Carry vs USA | -3.10 | 0.496 | 813 |
| REER (log) | -3.43 | 0.307 | 1,572 |
| REER (Δ%) | -2.01 | 0.286 | 1,540 |
| House prices (Δ%) | 0.92 | 0.625 | 1,499 |
| Stock mkt cap/GDP | 0.27 | 0.920 | 779 |
| Term spread | -5.83 | 0.357 | 781 |

Safe interest rates dominate: demographics explain the most variation in short and long rates, with standardized $Z_1$ coefficients an order of magnitude larger than for equity capitalization. This is consistent with the Kopecky-Taylor murder-suicide prediction.

### 7.2 Age Decomposition Across Assets

The old-age versus youth dependency decomposition provides additional insight:

| Asset Class | Old Dep | p | Youth Dep | p |
|---|---|---|---|---|
| Safe rate (10y) | -5.70*** | <0.001 | 5.81*** | 0.004 |
| Safe rate (3m) | -4.80*** | 0.003 | 6.16*** | 0.001 |
| Carry vs USA | -4.22*** | <0.001 | 3.14*** | 0.009 |
| House prices (Δ%) | 1.12** | 0.032 | 0.42 | 0.340 |
| Portfolio equity/GDP | 1.68* | 0.053 | -0.36 | 0.191 |
| Term spread | -0.80 | 0.593 | -3.21* | 0.079 |

Old-age dependency is the primary channel for safe rate depression and carry trade narrowing. Youth dependency has a marginally significant negative association with the term spread ($p = 0.079$), though the $Z$ polynomial is null — this may reflect that countries with large youth cohorts tend to have different monetary policy regimes rather than a direct demographic channel to the yield curve slope. Housing shows a significant old-age dependency effect in this standardized specification ($p = 0.032$), but as documented in Section 5.1, this collapses entirely when GDP per capita is added as a control — the demographic-housing association is spurious, driven by the income-aging confound. Portfolio equity positions respond to old-age dependency at marginal significance ($p = 0.053$), but the negative $R^2$ makes this descriptive rather than substantive (see Section 6.2).

### 7.3 Forward Projections

Using the latest demographic data and estimated coefficients, we compute mechanical partial-equilibrium projections of the demographic component ($Z_1 \hat\gamma_1 + Z_2 \hat\gamma_2 + Z_3 \hat\gamma_3$) for 15 focus countries. These projections hold all non-demographic factors constant and should be interpreted as indicating the *direction* and *relative magnitude* of demographic pressure, not as point forecasts. Housing is excluded from these projections given the null result documented in Section 5.

**Countries facing greatest safe rate compression (demographic pressure on 10y yields):**
- Japan: -4.13 percentage points
- Germany: -2.73 pp
- France: -2.55 pp
- Italy: -2.55 pp

**Countries facing upward rate pressure:**
- India: +2.65 pp
- South Africa: +2.24 pp
- Brazil: +2.20 pp
- Turkey: +1.98 pp

The demographic divergence in safe rates between aging and young economies exceeds 6 percentage points, creating persistent cross-country interest rate differentials that drive capital flows and exchange rate dynamics.

## 8. The Perfect Cancellation: Bridging Asset Returns and Fiscal Sustainability

### 8.1 Why r Falls but r-g Does Not

Our companion fiscal dominance paper finds that demographics have no significant effect on the interest-growth differential r-g (all Z coefficients p > 0.56), even as this paper documents that demographics strongly predict the *level* of safe rates (Z₁ = 45.6, p = 0.011). The implication is precise: demographics depress both r and g by nearly identical magnitudes, producing a "perfect cancellation" in the differential that governs debt dynamics.

This is not a mechanical artifact. The r channel operates through lifecycle portfolio rebalancing: as populations age, the shift from equities to bonds compresses safe yields. The g channel operates through labor force shrinkage and reduced dynamism: fewer workers mean lower potential output growth. These are theoretically distinct mechanisms — one is a financial market phenomenon, the other is a real-economy phenomenon — yet they produce offsetting effects on the single variable (r-g) that determines whether public debt is sustainable.

The cancellation has profound implications. For fiscal sustainability, it means the theoretical worry that aging triggers debt spirals through rising r-g is empirically unfounded — the fiscal threat from aging operates through the expenditure-revenue asymmetry (the "spending channel" documented in the fiscal dominance paper), not through adverse interest rate dynamics. For monetary policy, it means the natural rate of interest falls with aging, but so does the growth rate against which it is benchmarked, leaving the "neutral" monetary policy stance approximately unchanged in real terms. For asset allocation, it means that aging-economy bond investors face lower nominal returns but not necessarily lower returns relative to the real economy — the "murder" of safe returns is a nominal phenomenon that is partially offset in real terms by the demographic growth drag.

### 8.2 Safe Asset Supply: Does Public Debt Matter?

An alternative explanation for the demographic compression of safe rates is that aging economies face a shortage of safe assets rather than excess savings demand. If governments in aging economies issue insufficient debt relative to the savings supply, yields would fall even without a portfolio rebalancing channel. We test this by adding government debt-to-GDP from the fiscal dominance paper as a control variable.

Adding debt/GDP to the 10-year yield specification produces: Z₁ = 42.3 (p = 0.018), debt/GDP = 0.008 (p = 0.14). The demographic coefficient attenuates modestly (from 45.6 to 42.3, approximately 7%) but remains strongly significant, while debt/GDP is itself insignificant. Higher government debt does not raise yields in this sample — consistent with the "safe asset demand" interpretation where demographic savings absorb whatever supply governments provide. The attenuation is small enough to confirm that the Kopecky-Taylor portfolio rebalancing channel, not safe asset scarcity, is the primary mechanism.

This finding has a policy corollary. If governments in aging economies could credibly expand safe asset supply (issuing more debt or creating new safe instruments), they might partially alleviate yield compression. But our fiscal dominance paper shows they are already doing this — debt ratios are rising across aging economies — and yields continue to fall. The demand channel dominates the supply channel.

## 9. Robustness

We conduct several robustness checks, organized by the threat they address.

### 9.1 Standard Robustness

1. **OECD versus non-OECD subsamples**: Safe rate results are OECD-specific (all available bond yield data), while REER results are weak in both subsamples.

2. **5-year lagged demographics**: Strengthens safe rate results ($Z_1$ from $p = 0.011$ to $p < 0.001$), supporting causal interpretation.

3. **First-differenced specifications**: Demographics null in first differences ($R^2 = 0.654$ driven by $\Delta$inflation), confirming the level effect is structural rather than cyclical.

4. **Old-age versus youth dependency**: Both significantly predict safe rates in opposite directions, consistent with lifecycle theory.

5. **Post-GFC subsample**: Housing results disappear post-2010.

6. **Z-KAOPEN interactions**: Not significant for safe rates ($p > 0.69$) or equity ($p > 0.45$), but Z×NFA marginally significant for REER ($p \approx 0.05$-$0.08$).

### 9.2 Mechanism Discrimination: Investment/GDP and Growth Controls

The most important robustness test probes whether the demographic effect on safe rates reflects the Kopecky-Taylor portfolio rebalancing mechanism or supply-side natural rate dynamics. We run four specifications for each rate maturity:

For 10-year bond yields:

| Specification | $Z_1$ | p-value | R² | N |
|---|---|---|---|---|
| Baseline (full controls) | 45.6 | 0.011 | 0.124 | 803 |
| Z + GDP growth only | 44.5 | 0.012 | 0.129 | 907 |
| Z + GDP growth + investment/GDP | 51.9 | <0.001 | 0.235 | 907 |
| Full controls + investment/GDP | 48.4 | 0.007 | 0.155 | 803 |

$Z_1$ is stable or strengthens across all specifications. With only GDP growth and investment/GDP as controls, $Z_1$ reaches its strongest value (51.9, $p < 0.001$), while investment itself enters with a highly significant negative coefficient ($-0.180$, $p < 0.001$). The demographic polynomial captures portfolio and savings behavior that is not obviously mediated by contemporaneous investment.

For 3-month rates, the pattern is similar: $Z_1$ ranges from 53.9 to 64.3 across specifications, always significant at the 1% level. Investment/GDP is insignificant for 3-month rates when added alongside GDP growth ($p = 0.37$), but significant and positive ($+0.067$, $p = 0.02$) with full controls.

We emphasize that investment/GDP is an equilibrium object — it responds to the same demographic forces that drive savings — so this test is suggestive rather than definitive.

As an additional probe that avoids the bad-control concern, we control for expected GDP growth (WEO forward-looking forecasts), which is less contaminated by contemporaneous equilibrium responses. $Z_1$ *strengthens* when expected growth is added (from 45.6 to 50.7, $p = 0.004$ for 10-year yields; from 58.7 to 60.2, $p = 0.005$ for 3-month rates), confirming the demographic signal is not merely a growth proxy. Controlling for log output per worker attenuates $Z_1$ substantially (to 27.4, $p = 0.12$ for 10-year yields), but output per worker is itself heavily shaped by demographic structure — countries with large working-age shares have mechanically higher labor productivity — making this a bad control in the same spirit as investment/GDP.

The overall pattern across all growth/investment probes is consistent: $Z_1$ survives any control that is not itself a demographic outcome, supporting the demand-side Kopecky-Taylor interpretation.

### 9.3 Levels versus Differences and Cointegration

Our level specifications raise the standard concern about spurious regression between trending variables. We address this through three complementary tests.

**Unit roots.** Country-by-country ADF tests find no rejections of unit roots for $Z_1$ (0 of 237 countries at 5%) or real 10-year yields (0 of 23 countries). Both series are highly persistent within countries, as expected for slow-moving demographic structure and equilibrium interest rates.

**First differences.** The first-differenced specification ($\Delta Z \to \Delta r$) yields insignificant demographic coefficients ($R^2 = 0.665$ driven by $\Delta$inflation), with all $\Delta Z$ coefficients having $p > 0.9$. This null is expected rather than troubling: demographic structure changes by fractions of a percentage point per year, while interest rates fluctuate by hundreds of basis points around business cycles. The demographic effect operates through slow-moving levels — a plausible long-run equilibrium relationship — rather than year-to-year changes.

**Cointegration.** The Kao pooled residual ADF test strongly rejects no-cointegration ($t = -13.80$, $p < 0.001$), providing aggregate panel evidence that the level relationship is not spurious. Country-by-country Engle-Granger tests yield mixed results: 11 of 23 countries (48%) reject no-cointegration at 5%. The mixed country-level results are not surprising given the short time series available for many OECD economies (median $T \approx 35$), which limits the power of individual ADF tests. The pooled test, which exploits cross-sectional information, provides the stronger inference.

Taken together, these results support interpreting the level relationship as a cointegrating equilibrium: demographics and safe rates share a common stochastic trend, with deviations being mean-reverting. The first-difference null is consistent with this interpretation — the equilibrium adjustment is too slow to detect in annual changes but accumulates over decades.

### 9.4 Housing and GDP per Capita

The demographic polynomial is null for house price growth ($Z_1 = 35.5$, $p = 0.26$), with all three $Z$ components individually insignificant ($p > 0.24$). The age decomposition shows a marginal youth dependency association ($15.4$, $p = 0.087$) but old-age dependency is null ($-7.1$, $p = 0.37$). Adding log GDP per capita attenuates youth dependency from marginal to insignificant ($12.6$, $p = 0.21$) while old-age dependency barely changes ($-6.4$, $p = 0.43$). GDP per capita itself is not significant in this specification. Lagged age ratios show a stronger youth dependency effect ($21.6$, $p = 0.009$) that survives the GDP per capita control ($21.5$, $p = 0.02$), but this isolated youth effect does not constitute a coherent demographic channel — the $Z$ polynomial remains null, and the old-age dependency that drives results for safe rates is entirely absent. Housing should not be listed among the asset classes that respond to demographics.

### 9.5 Outlier Sensitivity: Portfolio Equity Positions

Portfolio equity/GDP significance is robust to dropping financial centers (Luxembourg, Singapore, Hong Kong, etc.) and to winsorization — $Z_1$ actually strengthens from $-298$ to $-336$. However, the negative $R^2$ persists across all specifications ($-0.017$ to $-0.044$), indicating the model captures a real cross-country pattern but has no overall explanatory power.

## 10. Conclusion

Demographics systematically predict safe interest rates across OECD economies but are null for equity market capitalization — consistent with the core asymmetry predicted by Kopecky and Taylor's "murder-suicide of the rentier" framework. We do not directly estimate the equity risk premium; rather, we test an implication of the framework for valuation proxies and institutional/international offset mechanisms. Working-age population shares ($Z_1$) are strongly associated with higher safe rates ($p < 0.01$), with the effect operating through slow-moving levels (lagged $Z$ strengthens results) rather than year-to-year changes (first differences are null). The demographic effect on rates is not obviously mediated by contemporaneous investment or growth potential — it survives controlling for investment/GDP and expected GDP growth across multiple specifications — consistent with the demand-side Kopecky-Taylor interpretation, though we note that investment/GDP is itself an equilibrium object so these tests are suggestive rather than definitive. The pooled panel cointegration test supports the level relationship ($t = -13.80$).

Three cross-paper consistencies, one important inconsistency, and one null emerge from placing these results alongside our companion multilateral and gravity papers. First, the rate channel is confirmed as OECD-specific and bond-yield-specific (lending rates remain null), consistent across all papers. Second, Z-KAOPEN interactions are null for domestic asset prices but highly significant for international flows — demographics affect rates regardless of openness, but openness gates the flow channel. Third, exchange rates play a minor role, consistent with the multilateral paper's estimate that the REER channel accounts for only 3.5% of the demographic effect on current accounts. The inconsistency concerns the term spread: it is a highly significant predictor of current accounts ($p < 0.001$) but is not itself predicted by demographics ($p = 0.39$), implying that its role in CA regressions reflects monetary policy or inflation credibility rather than a demographic channel — one of this paper's most informative findings. The null concerns housing: the demographic polynomial is insignificant for house price growth ($p = 0.26$), with only a marginal and isolated youth dependency association that does not constitute a coherent demographic channel. Portfolio equity positions show significant cross-country patterning but persistently negative $R^2$, which we treat as descriptive rather than substantive.

As global population aging accelerates, these findings imply persistent downward pressure on safe interest rates in advanced economies, with implications for monetary policy (the natural rate of interest), pension sustainability (the retirement income crisis), and international capital allocation (demographic-driven rate differentials driving capital from aging to young economies).

A final implication deserves emphasis. The murder of safe returns combined with the housing null creates a **retirement income challenge** for aging societies. Bond yields — the primary safe store of value for the middle class — are compressed by lifecycle portfolio rebalancing, while house prices show no independent demographic support. Equity markets are resilient, but equity ownership is concentrated among high-income households; the median retiree depends on bonds and housing. As populations age beyond the 15% OADR threshold identified in our Japanification paper, the rentier class faces erosion of its primary safe income source. Pension sustainability, already threatened by the expenditure-revenue asymmetry documented in our fiscal dominance paper, is further undermined by the collapse in safe returns that fund defined-benefit obligations. The murder-suicide of the rentier is not merely an asset pricing curiosity — it is a structural threat to retirement income security in every aging economy.

## 11. References

Higgins, M. (1998). Demography, national savings, and international capital flows. *International Economic Review*, 39(2), 343-369.

Koomen, M. (2021). Demographics and the current account. *IMF Working Paper*.

Kopecky, J., & Taylor, A. M. (2022). The murder-suicide of the rentier: Population aging and the risk premium. *NBER Working Paper No. 30011*.

Lane, P. R., & Milesi-Ferretti, G. M. (2007). The external wealth of nations mark II. *Journal of International Economics*, 73(2), 223-250.

Phillips, S., et al. (2013). The external balance assessment (EBA) methodology. *IMF Working Paper 13/272*.
